From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computers

TL;DR

This paper introduces a generalized diffusion framework that incorporates structured probabilistic sampling using p-computers, improving generative modeling by exploiting known interactions and correlations.

Contribution

It extends diffusion models by integrating MCMC dynamics with interaction structures, enabling more efficient and accurate sampling on probabilistic hardware.

Findings

Correlated diffusion yields samples closer to MCMC references.

Incorporating Ising couplings exploits spatial correlations.

p-computers significantly improve sampling throughput and energy efficiency.

Abstract

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current implementations usually place most computation in the neural network, but diffusion as a framework allows a broader range of choices for the stochastic transition kernel. Here, we generalize the stochastic sampling component by replacing independent noise injection with Markov chain Monte Carlo (MCMC) dynamics that incorporate known interaction structure. Standard independent diffusion is recovered as a special case when couplings are set to zero. By explicitly incorporating Ising couplings into the diffusion dynamics, the noising and denoising processes exploit spatial correlations representative of the target system. The resulting framework maps naturally onto probabilistic computers (p-computers) built from probabilistic bits (p-bits), which provide orders-of-magnitude advantages in sampling throughput and energy efficiency over GPUs. We demonstrate the approach on equilibrium states of the 2D ferromagnetic Ising model and the 3D Edwards-Anderson spin glass, showing that correlated diffusion produces samples in closer agreement with MCMC reference distributions than independent diffusion. More broadly, the framework shows that p-computers can enable new classes of diffusion algorithms that exploit structured probabilistic sampling for generative modeling.